A distributed singular perturbation algorithm in a non-cooperative game under limited control authority

• Published in: IFAC-PapersOnLine Vol. 51; no. 23; pp. 367 - 372
• Main Authors: Nguyen, Chuong Van, Hatanaka, Takeshi, Ahn, Hyo-Sung
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2018
• Subjects: Dynamic average consensus; Limited control authority; Non-cooperative game; Non-cooperative game; Dynamic average consensus; Limited control authority
• ISSN: 2405-8963; 2405-8963
• DOI: 10.1016/j.ifacol.2018.12.063

This paper proposes a distributed algorithm to seek Nash equilibrium (NE) in a non-cooperative game under limited control authority (LCA). Our proposed strategy relies upon singular perturbed system and dynamic average consensus algorithm. The distributed algorithm is designed so that every player can precisely estimate actions of other players in the game under the LCA, then follows a gradient-based method to reach NE. We also provide a convergence proof of the algorithm to a NE of the game. Numerical simulation is finally carried out to verify the effectiveness of our design.